Person: Morales González, Domingo
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First Name
Domingo
Last Name
Morales González
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Area
Estadística e Investigación Operativa
Identifiers
5 results
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Now showing 1 - 5 of 5
Item Approximations to powers of phi-disparity goodness-of-fit tests(Communications in statistics. Theory and methods, 2001) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro; Vadja, IgorThe paper studies a class of tests based on disparities between the real-valued data and theoretical models resulting either from fixed partitions of the observation space, or from the partitions by the sample quantiles of fixed orders. In both cases there are considered the goodness-of-fit tests of simple and composite hypotheses. All tests are shown to be consistent, and their power is evaluated at the nonlocal as well as local alternatives.Item Statistical inference for finite Markov chains based on divergences(Statistics and probability letters, 1999) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro; Zografos, KonstantinosWe consider statistical data forming sequences of states of stationary finite irreducible Markov chains, and draw statistical inference about the transition matrix. The inference consists in estimation of parameters of transition probabilities and testing simple and composite hypotheses about them. The inference is based on statistics which are suitable weighted sums of normed phi-divergences of theoretical row distributions, evaluated at suitable points, and observed empirical row distributions. The asymptotic distribution of minimum phi-divergence estimators is obtained, as well as critical values of asymptotically alpha-level tests.Item Tests based on divergences for and against ordered alternatives in cubic contingency tables(Applied Mathematics and Computation, 2003) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, LeandroCubic contingency tables arise frequently in medical sciences when individuals are measured before, during and after the application of some treatment for a given illness, and data are recorded on an ordered categorical scale. By assigning increasing values to the levels of the illness, the efficiency of the medical treatment can be checked by testing for a given ordering of the cell probabilities p(ijk)'s. One possibility is to consider the hypothesis H-1 that p(ijk) less than or equal to p(i'j'f') if and only if (i', j', k') can be obtained from (i, j, k) through successive pairwise interchanges of adjacent components resulting each time in a decreasing order of the two interchanged components. In this paper we introduce two families of divergence statistics to test for and against H-1, and their asymptotic distributions are obtained. It is also shown that likelihood-ratio test statistics of Barmi and Zimmermann [Statist. Prob. Lett. 45 (1999) 1] are included in these families.Item Minimum divergence estimators based on grouped data(Annals of the Institute of Statistical Mathematics, 2001) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro; Vadja, IgorThe paper considers statistical models with real-valued observations i.i.d. by F(x, theta (0)) from a family of distribution functions (F(x, theta); theta is an element of Theta), Theta subset of R-s, s greater than or equal to 1. For random quantizations defined by sample quantiles (F-n(-1)(lambda (1)),..., F-n(-1)(lambda (m-1))) of arbitrary fixed orders 0 < (1) < ... < lambda (m-1) < 1, there are studied estimators (phi ,n) of theta (0) which minimize phi -divergences of the theoretical and empirical probabilities. Under an appropriate regularity, all these estimators are shown to be as efficient (first order, in the sense of Rao) as the MLE in the model quantified nonrandomly by (F-1(lambda (1), theta (0)),..., F-1(lambda (m-1), theta (0))). Moreover, the Fisher information matrix I-m(theta (0), lambda) of the latter model with the equidistant orders lambda = (lambda (j) = j/m : 1 less than or equal to j less than or equal to m-1) arbitrarily closely approximates the Fisher information F(theta (0)) of the original model when m is appropriately large. Thus the random binning by a large number of quantiles of equidistant orders leads to appropriate estimates of the above considered type.Item φ-divergences and nested models.(Applied Mathematics Letters, 1997) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, LeandroWe consider a wide class of statistics, namely phi-divergences. We obtain asymptotic distributions of these statistics in nested models. Our result generalizes previous results in this field.